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A202107 n^4*(n+1)^4/8. 1
2, 162, 2592, 20000, 101250, 388962, 1229312, 3359232, 8201250, 18301250, 37949472, 74030112, 137149922, 243101250, 414720000, 684204032, 1095962562, 1710072162, 2606420000, 3889620000, 5694792642, 8194304162, 11605565952, 16200000000, 22313281250, 30356972802 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A relation between fourth powers and the sum of fifth and seventh powers. See the first formula, which is from Beiler.

REFERENCES

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 161.

LINKS

Table of n, a(n) for n=1..26.

Temple Rice Hollcroft, On sums of powers of n consecutive integers, Bulletin of the American Mathematical Society 59 (1953), nr. 6, p. 526 (574t).

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1)

FORMULA

a(n) = 2*sum(k, k=1..n)^4 = sum(k^5 + k^7, k=1..n).

a(n) = 2*A059977(n-1).

a(n) = A000539(n) + A000541(n).

G.f. -2*x*(1+72*x+603*x^2+1168*x^3+603*x^4+72*x^5+x^6) / (x-1)^9. - R. J. Mathar, Dec 13 2011

a(n) = 2*(A000217(n)^4). - Moshe Levin, Jan 21 2012

MAPLE

A202107:=n->(n^4)*(n+1)^4/8; seq(A202107(n), n=1..100); # Wesley Ivan Hurt, Nov 12 2013

MATHEMATICA

Table[n^4 (n+1)^4/8, {n, 100}] (* Wesley Ivan Hurt, Nov 12 2013 *)

CROSSREFS

Cf. A000217, A000539, A000541, A059977.

Sequence in context: A272244 A178575 A069580 * A109420 A162904 A259319

Adjacent sequences:  A202104 A202105 A202106 * A202108 A202109 A202110

KEYWORD

nonn,easy

AUTHOR

Martin Renner, Dec 11 2011

STATUS

approved

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Last modified December 5 03:20 EST 2016. Contains 278755 sequences.